# Cool roots.#Pythagorean

Algebra Level 5

given that $P(x)= x^3 +ax^2 +bx-14760$ has integral roots $$\alpha,\beta,\gamma$$ such that $\alpha^2 +\beta^2 =\gamma^2$ find $$P(10)$$ $$mod$$ $$88$$. $$details$$ & $$assumption$$ $0\ne|\alpha|<|\beta|<|\gamma|, \alpha<\beta<\gamma$ work with the maximum value of $$\alpha,\beta,\gamma$$

All roots are positive.

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